Bài 3:
1: \(\left(3x^2-4\right)\left(x+3y\right)=3x^3+9x^2y-4x-12y\)
2: \(\left(x+3\right)\left(x^2+3x\right)=x\cdot\left(x+3\right)^2\)
\(=x\left(x^2+6x+9\right)=x^3+6x^2+9x\)
3: \(\left(xy-1\right)\left(xy+5\right)=x^2y^2+5xy-xy-5=x^2y^2+4xy-5\)
4: \(\left(3x+5y\right)\left(2x-7y\right)\)
\(=6x^2-21xy+10xy-35y^2\)
\(=6x^2-11xy-35y^2\)
5: \(-\left(x-1\right)\left(-x^2+2y\right)=\left(x-1\right)\left(x^2-2y\right)\)
\(=x^3-2xy-x^2+2y\)
6: \(\left(-x^2+2y\right)\left(x^2+2y\right)\)
\(=-x^4-2x^2y+2x^2y+4y^2=4y^2-x^4\)
7: \(\left(x+3y\right)\left(x-3y+2\right)\)
\(=\left(x+3y\right)\left(x-3y\right)+2\left(x+3y\right)\)
\(=x^2-9y^2+2x+6y\)
8: \(\left(x+2y\right)\left(x-2y+3\right)\)
\(=\left(x+2y\right)\left(x-2y\right)+3\left(x+2y\right)\)
\(=x^2-4y^2+3x+6y\)
9: \(\left(x^2-xy+y^2\right)\left(x+y\right)\)
\(=x^3+x^2y-x^2y-xy^2+xy^2+y^3\)
\(=x^3+y^3\)
10: \(\left(x^2-xy+y^2\right)\left(x+y\right)=x^3+y^3\)
11: \(\left(5x-2y\right)\left(x^2-xy+1\right)\)
\(=5x^3-5x^2y+5x-2x^2y+2xy^2-2y\)
\(=5x^3-7x^2y+2xy^2+5x-2y\)
12: \(\left(x^2y^2-xy+y\right)\left(x-y\right)\)
\(=x^3y^2-x^2y^3-x^2y+xy^2+xy-y^2\)
13: \(\left(x^2-2xy+y^2\right)\left(x-y\right)=\left(x-y\right)^3=x^3-3x^2y+3xy^2-y^3\)
14: \(-\left(x-y\right)\left(x^2+xy-1\right)\)
\(=\left(-x+y\right)\left(x^2+xy-1\right)\)
\(=-x^3-x^2y+x+x^2y+xy^2-y\)
\(=-x^3+x+xy^2-y\)
15: \(-\left(x^2-2y\right)\left(x+y^2-1\right)\)
\(=\left(-x^2+2y\right)\left(x+y^2-1\right)\)
\(=-x^3-x^2y^2-x^2+2xy+2y^3-2y\)
16: \(\)\(\left(\dfrac{1}{2}x-1\right)\left(2x-3\right)=x^2-\dfrac{3}{2}x-x+3=x^2-\dfrac{5}{2}x+3\)
17: \(\left(x-\dfrac{1}{2}y\right)\left(x-\dfrac{1}{2}y\right)=\left(x-\dfrac{1}{2}y\right)^2\)
\(=x^2-2\cdot x\cdot\dfrac{1}{2}y+\left(\dfrac{1}{2}y\right)^2\)
\(=x^2-xy+\dfrac{1}{4}y^2\)
18: \(\left(x^2-2x+3\right)\left(\dfrac{1}{2}x-5\right)\)
\(=\dfrac{1}{2}x^3-5x^2-x^2+10x+\dfrac{3}{2}x-15\)
\(=\dfrac{1}{2}x^3-6x^2+11,5x-15\)
Bài 4:
1: \(x^2\left(x-1\right)-\left(x^2+1\right)\left(x+2\right)\)
\(=x^3-x^2-x^3-2x^2-x-2\)
\(=-3x^2-x-2\)
2: \(x\left(x-y^2\right)-\left(x^2-y\right)\left(y+1\right)\)
\(=x^2-xy^2-x^2y-x^2+y^2+y\)
\(=-xy^2-x^2y+y\)
3: \(\left(x-5\right)\left(x^2+26\right)+\left(5-x\right)\left(1-5x\right)\)
\(=x^3+26x-5x^2-130+5-25x-x+25x^2\)
\(=x^3+20x^2-125\)
4: \(\left(x-y\right)\left(x^2+y\right)-\left(x-1\right)\left(x^2+y^2\right)\)
\(=x^3+xy-x^2y-y^2-x^3-xy^2+x^2+y^2\)
\(=-x^2y+x^2+xy-xy^2\)
ai giải giúp em từ 3 đến bài 12 với ạ em đang cần gấp chiều em đi thi ạ
Giúp em bài 4 với cả bài 5 với ạ
